Ubuningi befiziksi ekunyakazeni okujikelezayo

Inani le-physics ekuhambeni okujikelezayo lihlanganisa ukufuduka kwe-angular, ijubane le-angular, kanye nokusheshisa kwe-angular.

1. Ukufuduka kwe-Angular (θ)

Ukufuduka endaweni ethile ngokunyakaza okujikelezayo kubizwa ngokuthi ukufuduka kwe-angular. Ngakho-ke, ukufuduka kwe-angular okuhlanganisa nobuningi be-vector kunesilinganiso kanye nesiqondiso. Isiqondiso sokufuduka kwe-angular sivame ukuvezwa ngendlela yewashi (ngokwewashi noma ngokuphambene newashi).

Kunezinhlobo ezintathu zokushintsha kwe-angular. Okokuqala, idigri (o). Umjikelezo owodwa wendilinga ulingana no-360^o. Okwesibili, ukuguquka. Umjikelezo owodwa wendilinga ulingana nokuguquka okukodwa. Okwesithathu, ama-radian. Bheka isithombe esingezansi. Uma into ihamba ngendilinga khona-ke u-r = irediyasi yendilinga, u-x = ubude bendlela eyindilinga edlula kuyo into = umjikelezo wendilinga.

Umjikelezo owodwa wendilinga ulingana nama-radian angu-2π.

Inkinga yesampula 1:

Uguquko olu-1 = 360^o. ½ inguquko = …. Rad?

Isixazululo:

Uguquko olu-1 = 360^o = 2 π rad = 2(3.14) rad = 6.28 rad

Uguquko lwe-1⁄2 = 180^o = 1⁄2 (6.28 rad) = 3.14 rad

Inkinga yesampula 2:

I-rad eli-1 = …… ^o 1^o = … rad?

Isixazululo:

180^o = π rad = 3.14 rad

2. Isivinini se-Angular (ω)

a. Isivinini Esimaphakathi Se-Angular

Inkinga yesampula 3:

Isondo lijikeleza ngokwewashi, lijikeleza i-engeli engu-180^o imizuzwana emi-2 kanye nama-90^o umzuzwana owodwa. Ungakanani ubukhulu kanye nesiqondiso sejubane elimaphakathi le-angular?

Isixazululo:

Isiqondiso sejubane elimaphakathi le-angular = isiqondiso esihambisana newashi.

9 ^o/s = … rad/s ?

Inkinga yesampula 4:

Isondo lijikeleza ngokwewashi, lijikeleza nge-engeli engu-360^o imizuzwana emi-4. Isondo libe selijikeleza ngokuphambene newashi, lijikeleza nge-engeli engu-180^o imizuzwana emi-2. Iyini ijubane elimaphakathi le-angular?

Isixazululo:

Isiqondiso sejubane elimaphakathi le-angular = isiqondiso esihambisana newashi.

3 ^o/s = … rad/s?

b. Isivinini se-angular esisheshayo

Ijubane le-angular elisheshayo livame ukubizwa ngokuthi ijubane le-angular. Uma kukhulunywa ngejubane le-angular kuphela, khona-ke okushiwoyo ijubane le-angular elisheshayo. Ubukhulu bejubane le-angular elisheshayo = ubukhulu bejubane le-angular ngesikhathi esifushane kakhulu. Ngokwezibalo:

Uma sisekuhambeni okuqondile, singashintsha ubukhulu bejubane ngesivinini, ukuze ekuhambeni okujikelezayo sikwazi ukushintsha ubukhulu bejubane le-angular ngejubane le-angular.

3. Ukusheshisa kwe-Angular (α)

a. Ukusheshisa okumaphakathi kwe-angle

Inkinga yesampula 5:

Ekuqaleni umshini womoya wawuphumulile, upheshulwa umoya, ngakho wajika ngokwewashi. Ngemva kwemizuzwana emi-2, ijubane le-angular liba ngu-90 ^o/s. Iyini isivinini esimaphakathi se-angular?

Isixazululo:

Ngokwesilinganiso, ijubane le-angular le-windmill lishintsha ama-o/second angu-45 njalo ngomzuzwana o-1 = … rad / s njalo ngomzuzwana o-1?

b. Ukusheshisa kwe-angular okusheshayo

Ukusheshisa kwe-angular okusheshayo kuvame ukufushaniswa ngokuthi ukusheshisa kwe-angular. Ukusheshisa kwe-angular okusheshayo kuwushintsho kwijubane le-angular ngesikhathi esifushane kakhulu. Ngokwezibalo:

Ubukhulu obuqondile ekunyakazeni okujikelezayo

Amanani aqondile angamanani ahambisanayo, njengokufuduka (ibanga), ijubane (isivinini), kanye nokusheshisa. Ngakolunye uhlangothi, amanani okunyakaza okujikelezayo angabizwa ngokuthi amanani ajikelezayo.

1. Ukufuduka

Bheka into ejikelezayo, njengesondo noma ifeni noma umshini womoya noma iwashi, njll. Uma into efana nefeni ijikeleza, zonke izingxenye zefeni ziyajikeleza ndawonye. Uma ifeni ijikeleza kanye (360)^o), bese zonke izingxenye zefeni, zombili ezitholakala onqenqemeni naseduze kwe-axis nazo zithatha umjikelezo owodwa noma u-360^o. Uguquko olulodwa noma u-360^o ubukhulu bokufuduka kwe-angular okwenziwa yizo zonke izingxenye zefeni, kokubili onqenqemeni naseduze kwe-axis.

Uma ifeni ithatha umjikelezo owodwa, ingxenye yefeni esemaphethelweni kanye nengxenye yefeni eduze kwe-axis yokujikeleza inyakaza kuze kufike esiyingini esisodwa (2). Uma i-radius yefeni ingu-20 cm, ibanga eliphakathi komphetho wefeni kanye ne-axis yokujikeleza lingu-20 cm. Isibonelo, ibanga eliphakathi kwe-axis kanye nengxenye eyodwa yefeni eseduze ne-axis = 1 cm. Uma ifeni yenza umjikelezo owodwa, umphetho wefeni uhamba ngokuzungeza kuze kufike ku-(2)(3.14)(20 cm) = 125.6 cm,

kuyilapho iphuzu eliseduze ne-axis lihamba ngokuzungeza kuze kufike ku-(2)(3.14)(1 cm) = 6.28 cm. 125.6 cm ubukhulu bokufuduka okwenziwa unqenqema lwefeni,

kuyilapho u-6.28 cm ubukhulu bokufuduka okwenziwe yiphuzu eliseduze ne-axis yokujikeleza. Uma u-r omncane, kulapho ukufuduka kuba kuncane khona. Ubudlelwano phakathi kokufuduka (d) kanye nokufuduka kwe-angular (θ) buvezwa yi-equation:

θ = d / r

d = r θ

d = ukufuduka (amamitha), r = irediyasi noma ibanga ukusuka ku-axis yokujikeleza (amamitha), θ = ukufuduka kwe-angular (ama-radian)

Inkinga yesampula 6:

I-CD engama-5 cm ku-radius ijikeleza nge-engeli engama-90o. Iyini i-displacement yephuzu elingu-2 cm ukusuka ku-axis yokujikeleza?

Isixazululo:

r = ibanga ukusuka ku-axis yokujikeleza = 2 cm = 0.02 m

θ = 90^o = 1.57 i-rad (kumele ishiwo ngama-radians)

d = (0.02 m)(1.57 rad) = 0.03 m.

Ukufuduka kwe-Angular akunayo iyunithi yesistimu yamazwe ngamazwe futhi akunaso isayizi (isayizi yayo ingu-1), ngakho-ke ekubalweni njengoba ngenhla, vele ususe iyunithi yama-radians emiphumeleni yokubala.

2. Isivinini

Uma ijikeleziswa, ifeni noma noma iyiphi into ejikelezayo, vele, idinga isikhawu esithile sesikhathi. Uma ifeni ijikeleza ngokwewashi futhi ithatha ukujikeleza okukodwa (360^o) umzuzwana owodwa,

khona-ke ijubane le-angular lazo zonke izingxenye zefeni lingu-1 rev/s = 360 ^o/s = 6.28 rad/s futhi isiqondiso sejubane le-angular sifana nesiqondiso senaliti yehora.

Uma irediyasi yefeni ingu-20 cm, khona-ke unqenqema lwefeni luhamba ngokuzungeza ngesivinini esingu-2(3.14)(20 cm) / umzuzwana o-1 = 125.6 cm/s = 1.256 m/s. Iphuzu eliyi-1 cm (0.01 m) ukusuka ku-axis yokujikeleza ngesivinini esingu-2 (3.14) (1 cm)/umzuzwana o-1 = 6.28 cm/s = 0.0628 m/s. Uma i-r encane, isivinini sincane. Ekunyakazeni okuzungezayo, isivinini sivame ukubizwa ngokuthi isivinini se-tangential.

Ubudlelwano phakathi kwejubane (v) kanye nejubane le-angular (ω) buvezwa yi-equation:

v = isivinini (m/s), r = irediyasi noma ibanga ukusuka ku-axis yokujikeleza (m), ω = ijubane le-angular (rad/s)

Inkinga yesampula 7:

Ijubane lenaliti yesibili lingu-6.28 rad/minute = 6.28 rad / 60 second = 0.1 rad/s. Iyini ijubane lephuzu elingama-2 cm (0.02 m) ukusuka ku-axis yokujikeleza?

Isixazululo:

ω = 0.1 rad/s, r = 0.02 m

v = r

ω = (0.02 m)(0.1 rad/s) = 0.002 m/s

Susa ama-radian emiphumeleni yokubala.

3. Ukusheshisa

Iphuzu elijikelezayo elijikelezayo liyashesha uma ubukhulu kanye nesiqondiso sejubane kushintsha. Ngakho-ke, kunezinhlobo ezimbili zokusheshisa ekuhambeni okujikelezayo. Okokuqala, ukusheshisa okuphakathi nendawo (a_c) noma okubizwa nangokuthi ukusheshisa kwe-radial (a_r). Ukusheshisa kwe-centripetal kwenzeka ngenxa yezinguquko endleleni yejubane. Indlela yokusheshisa kwe-centripetal ihlala iya enkabeni yendilinga.

Ubukhulu bokusheshisa kwe-centripetal yilokhu:

a_c = ukusheshisa kwe-centripetal (m/s)²), r = irediyasi noma ibanga ukusuka ku-axis yokujikeleza (m), v = isivinini (m/s), ω = ijubane le-angular (rad/s)

Okwesibili, ukusheshisa okubonakalayo (a_t). Ukusheshisa okuqondile kwenzeka ngenxa yezinguquko ngobukhulu bejubane. Buyekeza iphuzu emaphethelweni efeni elijikelezayo. Uma, ekuqaleni, ifeni iphumule, khona-ke iphuzu emaphethelweni efeni nalo liphumule (v = 0). Uma umzuzwana owodwa kamuva, ifeni ijikeleza ngesivinini se-angular esingu-1 rev/s = 360 ^o/s = 6.28 rad/s ukuze iphuzu eliseceleni kwefeni lihambe ngokuzungeza ngesivinini esingu-1.2 m/s

bese iphuzu eliseceleni komoya wefeni lizwa ukusheshisa okuqondile okungu-1.2 m/s ngomzuzwana = 1.2 m/s².

Ubudlelwano phakathi kokusheshisa kwe-tangential (a_t) kanye nokusheshisa kwe-angular (α) kuvezwa yi-equation:

a_t = ukusheshisa kwe-tangential (m/s²), r = irediyasi noma ibanga ukusuka ku-axis yokujikeleza (m), α = ukusheshisa kwe-angular (rad/s²)

Ubudlelwano phakathi kwesikhathi (T) kanye nemvamisa (f) nesivinini kanye nesivinini se-angular

Inkathi isho isikhathi lapho into izokwenza uguquko olulodwa, kuyilapho uguquko lusho inani loguquko lomzuzwana owodwa. Ubudlelwano phakathi kwenkathi nophindaphindo buvezwa ngesibalo: f = 1/T

Iyunithi yeSistimu Yomhlaba Wonke yesikhathi ingeyesibili, iyunithi yeSistimu Yomhlaba Wonke yemvamisa ingu-1 / umzuzwana (= i-hertz). Isivinini (v) kanye nesivinini se-angular (ω) sezinhlayiya ezihambayo eziyindilinga zingavezwa ngezikhathi noma amaza.

Ijubane (v) lenhlayiya ehambayo eyindilinga livezwa yi-equation:

Ubukhulu bejubane le-angular (ω) lezinhlayiya ezihambayo eziyindilinga buvezwa yi-equation: